Details

sample274.0ms

Algorithm

intervals

Results

133.0ms	59×	body	2560	valid
79.0ms	74×	body	1280	valid
28.0ms	60×	body	640	valid
13.0ms	36×	body	320	valid
3.0ms	12×	body	160	valid
2.0ms	15×	body	80	valid

simplify31.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	16
3	16
2	14
1	11
0	6

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize107.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
1.8b	(- 1.0 (cos x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 70

Calls

2 calls:

43.0ms	(/ (- 1.0 (cos x)) (sin x))
29.0ms	(- 1.0 (cos x))

series104.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- 1.0 (cos x)) (sin x))
31.0ms	(- 1.0 (cos x))

simplify4.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	2324
2	768
1	310
0	136

prune908.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/240 (pow x 5) (* x (fma (* x 1/24) x 1/2)))
0.0b	(fma (* x 1/24) x 1/2)
0.1b	(* x (fma (* x 1/24) x 1/2))
0.4b	(* x 1/24)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 66

Calls

4 calls:

3.0ms	(fma 1/240 (pow x 5) (* x (fma (* x 1/24) x 1/2)))
3.0ms	(fma (* x 1/24) x 1/2)
20.0ms	(* x (fma (* x 1/24) x 1/2))
15.0ms	(* x 1/24)

series403.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(fma 1/240 (pow x 5) (* x (fma (* x 1/24) x 1/2)))
117.0ms	(fma (* x 1/24) x 1/2)
125.0ms	(* x (fma (* x 1/24) x 1/2))
33.0ms	(* x 1/24)

simplify5.6s

Counts

78 → 78

Iterations

Iter	Nodes
done	5028
3	2024
2	471
1	191
0	94

prune872.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize149.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/240 (pow x 5) (+ (* x (* (* x 1/24) x)) (* x 1/2)))
0.1b	(* (* x 1/24) x)
0.1b	(* x (* (* x 1/24) x))
0.4b	(* x 1/24)

rewrite242.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

3.0ms	(fma 1/240 (pow x 5) (+ (* x (* (* x 1/24) x)) (* x 1/2)))
38.0ms	(* (* x 1/24) x)
156.0ms	(* x (* (* x 1/24) x))
37.0ms	(* x 1/24)

series215.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma 1/240 (pow x 5) (+ (* x (* (* x 1/24) x)) (* x 1/2)))
41.0ms	(* (* x 1/24) x)
55.0ms	(* x (* (* x 1/24) x))
25.0ms	(* x 1/24)

simplify11.0s

Counts

89 → 89

Iterations

Iter	Nodes
done	5001
3	4531
2	806
1	247
0	100

prune921.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

localize95.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (cos x)) (sin x))
0.2b	(exp (/ (- 1.0 (cos x)) (sin x)))
1.4b	(log (exp (/ (- 1.0 (cos x)) (sin x))))
1.8b	(- 1.0 (cos x))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
40×	`add-cube-cbrt`
38×	`exp-prod`
20×	`log-pow`
11×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
7×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`log-prod` `associate-/r*` `fma-neg` `div-sub` `div-inv`
2×	`flip3--` `exp-diff` `flip--` `associate-/l/`
1×	`cbrt-undiv` `log-div` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `rem-exp-log`

Counts

4 → 136

Calls

4 calls:

46.0ms	(/ (- 1.0 (cos x)) (sin x))
55.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
70.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
19.0ms	(- 1.0 (cos x))

series370.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- 1.0 (cos x)) (sin x))
124.0ms	(exp (/ (- 1.0 (cos x)) (sin x)))
109.0ms	(log (exp (/ (- 1.0 (cos x)) (sin x))))
43.0ms	(- 1.0 (cos x))

simplify4.9s

Counts

148 → 148

Iterations

Iter	Nodes
done	5005
3	2528
2	884
1	392
0	199

prune1.3s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 0.1b

regimes778.0ms

Accuracy

98.5% (0.5b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 32.5b

bsearch5.0ms

simplify25.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample9.7s

Algorithm

intervals

Results

4.0s	2750×	body	1280	valid
3.8s	1531×	body	2560	valid
1.2s	1947×	body	640	valid
369.0ms	906×	body	320	valid
124.0ms	498×	body	160	valid
51.0ms	364×	body	80	valid
14.0ms	4×	body	5120	valid